The interaction between non-trivial topological states and the magnetic order of intrinsic magnetic topological insulators gives rise to various exotic physical properties,including the quantum anomalous Hall effect and axion insulator, etc. These materials hold great potential for application in low-power topological spintronic devices and topological quantum computation. Since the discovery of the first intrinsic magnetic topological insulator, MnBi<sub>2</sub>Te<sub>4</sub>, in 2019, this material system has garnered significant attention from researchers and sparked a research boom. This paper begins by discussing the fundamental properties of MnBi<sub>2</sub>Te<sub>4</sub> and then delves into important research findings related to this intrinsic magnetic topological insulator. Specifically, it focuses on the quantum anomalous Hall effect, axion insulating state, and Majorana zero energy mode exhibited by the MnBi<sub>2</sub>Te<sub>4</sub> series. Furthermore, the paper highlights other research directions and current challenges associated with this material system. Finally, the paper provides a summary and outlook for future research on MnBi<sub>2</sub>Te<sub>4</sub>, aiming to offer valuable references for researchers in related fields.